Entanglement entropies in free-fermion gases for arbitrary dimension
Dipartimento di Fisica dell'Università di Pisa and INFN - Pisa, Italy, EU
Accepted: 6 December 2011
We study the entanglement entropy of connected bipartitions in free-fermion gases of N particles in arbitrary dimension d. We show that the von Neumann and Rényi entanglement entropies grow asymptotically as N(d−1)/d ln N, with a prefactor that is analytically computed using the Widom conjecture both for periodic and open boundary conditions. The logarithmic correction to the power-law behavior is related to the area-law violation in lattice free fermions. These asymptotic large-N behaviors are checked against exact numerical calculations for N-particle systems.
PACS: 05.70.Jk – Critical point phenomena / 03.67.Mn – Entanglement measures, witnesses, and other characterizations / 71.10.Ca – Electron gas, Fermi gas
© EPLA, 2012